AuthorTopic: Explanation of decibels in the context of ADSL (Read 70144 times)

I just came across this document which I put together a couple of years ago. It attempts to explain what decibels are and how they relate to ADSL connections.

-----------------------------------------------------------------------------------------------------------------Attenuation, SNR and decibelsThis is an attempt to explain what these terms actually mean, and their significance for broadband performance.

The decibel---------------The decibel is a logarithmic unit which specifies the ratio of two powers. It was devised by the Bell Telephone Company to simplify calculations of gain and loss in cascaded transmission systems. The original unit was the Bel, and they defined this as:

Number of Bels = logarithm (base 10) of the ratio OutputPower / InputPower.

Because this was rather too coarse a unit for many purposes, they specified the decibel (dB) as one tenth of a Bel.This may seem a rather cumbersome way of specifying a power gain or loss, but it has some advantages:

1. Because of the way that logarithms work, the overall gain of several cascaded stages is simply the sum of the decibel gains of each stage. This is a lot easier than multiplying and dividing the power ratios.2. The log of a number less than 1 is negative, so all power gains have positive dB values and all losses have negative dB values. If the input and output powers are equal, then the gain is 0 dB.

Attenuation--------------Ordinary twisted-pair telephone lines were never designed for the high frequencies used in ADSL transmission. Not surprisingly a lot of the ADSL signal gets lost between the exchange and the user. What may surprise you is just how much gets lost...

Prior to 6 September 2004, the limiting attenuation figure for a UK ADSL installation was 60 dB (i.e. a gain of -60 dB). This is equal to 6 Bels, and therefore the logarithm of the power ratio is 6. In other words, the signal at the end of the line is just one-millionth of the signal transmitted from the exchange. And as from 6/9/2004 the limits were relaxed further, with 75 dB being the level of attenuation at which a usable ADSL service is considered extremely unlikely - that's a power ratio of about 32 million. Lower levels of attenuation are obviously preferable.

Signal-to-noise ratio-------------------------Just to make life even more complicated for the receiving equipment, spurious signals get induced into the lines carrying the ADSL signal. These spurious signals can come from other telephone lines running alongside, from external electrical sources, from poor quality connections, and from electronic circuits processing the signals. Together, these unwanted signals are referred to as 'noise'. Clearly, to enable the receiving equipment to separate the wanted signal from the noise, the wanted signal must be greater than the noise by a reasonable margin. The ratio between the wanted and unwanted signals is called the signal-to-noise ratio, or SNR. The greater this ratio is, the better.

The limiting value of SNR is generally taken to be 6 dB (= 0.6 Bel). This corresponds with a power ratio of 4 (log 4 = 0.6). So the wanted signal power must be at least four time the noise power. And because power is proportional to the square of the voltage, this means that the signal voltage must be at least double the noise voltage. Quite obviously, any lower values of SNR will make it very difficult to separate out a clean ADSL signal.

It should be noted that ADSL modems and routers generally report noise margin, not SNR. The manufacturer specifies a SNR at which the error count reaches some threshold beyond which the connection would not be acceptably stable; the noise margin is the amount by which the measured SNR exceeds this base level of SNR. So, for example, if the minimum acceptable SNR was set at 6 dB, and the measured SNR was 10 dB, then the modem/router would report a noise margin of 4 dB.-------------------------------------------------------------------------------------------------------------------------

Ooh, nice one Eric That's one of the best ways I've ever seen it described.

The one thing that makes me chuckle is when people say (and I've been guilty of it myself too!) "oh look, my SNR is only 3 or 4 dB different to yours"... not realising that a 3dB gain actually means twice the power or 1.41 times the voltage - a significant change!

One thing I would say is that you might want to cover SNR Margin, which ADSL modems report, rather than absolute SNR? Just a thought..

guest

As an ex-electronics engineer who specialised in radar I'd like to point out that dB measurements are meaningless unless you reference what the measurement is based upon.

eg a dBm would usually be a reference against a milliwatt of power at the source. Which brings the question of power and voltage into play (voltage is 20 Log and power is 10 Log) but that is just going to confuse most of you - no offence intended.

I could come up with a dB measurement which would sound incredible - but what is the baseline? dB on its own means nothing - it is what it is referenced to that is important.

Edit - rule of thumb is that a loss of 3dB halves the power. So 6dB = quarter the source power, 9dB = an eighth etc etc

Edit 2 - may seem like I'm a "know it all"? I don't but I do know dB measurements as defence contractors stretch radar detection "specs" to the limit (and beyond) so I do know how to "manipulate" the figures.

To be fair to Eric the title does state "in the context of ADSL". One can go to PhD level and beyond with one's explanations, but that would tend overload/send to sleep a high proportion of your intended audience.

As I said, above, the beauty of this site is that it (mostly) imparts technical information in plain English.

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guest

Quite true. I mention it only because I had a hell of a time finding out what BT referenced their measurements to - I think it took 3 or 4 months before either I or Mr S on adslguide could find anyone in BT Wholesale (as was) who knew what the baseline was. It's a milliwatt (or it was) if anyone is interested

If nothing else you should all remember that 3dB more attenuation (power) halves the signal strength and each additional 3dB halves it again - logarithmic you see. Start working out what 45dB and 60dB (old BT wholesale cutoff figures) actually are in power terms and you'll perhaps see how incredible it is that some people get a connection at all.

It is also possible to discriminate (detect and use) signals below the noise floor. ie you could have a 0dB connection which worked. Not with consumer router/modems though for the filters (electronic, not passive) would cost £100 on their own

Just to be clear about this, decibels are a ratio not an absolute measurement. dB measurements aren't meaningless when used in the way I defined them above, i.e. as a ratio of two different power levels. Attenuation and SNR are both ratios, not absolute measurements. So while your point is correct, it doesn't (with respect) apply to what I wrote above.

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Eric

guest

Fair enough Eric - I spose for the average user it doesn't. Like I said though it took a bit of work to get the reference point BT used - at one point they told me it was dBW. I suggested they may wish to go into the central heating business as 13k lines with 25% ADSL enabled = 3-4kW I suspect that'd give Openreach even more faults than now

Everyone just remember that every extra 3dB = half the signal. Useful rule of thumb. Always was for me when working out how far to stand away from radomes anyway <can't find a smiley being zapped kitz?>

Twas just a suggestion - as you say dB is a ratio but ask any engineer (real engineers rather than technicians called engineers) about it and they will say the same thing. A "ratio" is meaningless unless you know what the "ratio" is measured against.

Seriously though this forum is perhaps a bit more less techy than some - crikey you lost me cause Im no electronics person - and probably way more relaxed about certain things since most of the people asking for help need things pretty low key. Ive managed to ramble on about stuff more than a few times not realising that I'd perhaps taken it a bit too deep for whom Im trying to respond to and stuff has gone way over their head

guest

The best thing really to remember (again!) is that the 3dB point on any signal is the point at which the signal has halved in power. It does bring the problem of long lines into very clear perspective.

Eg I have a 23dB figure on downstream - that means that the 1 milliwatt (one thousandth of a watt) which comes from the DSLAM is actually somewhere around 50 microwatts* (50 millionths of a watt) when it gets here. That gets me 20Mbps. I still find that amazing and I used to design radar systems

*I'm doing that in my head - seems roughly right but correct me if you think its wrong (it may be)

Twas just a suggestion - as you say dB is a ratio but ask any engineer (real engineers rather than technicians called engineers) about it and they will say the same thing. A "ratio" is meaningless unless you know what the "ratio" is measured against.

I'm sorry to labour the point, but none of this is relevant to the article at the top of this thread. A ratio is not meaningless, it's what it says - a ratio, i.e. one number divided by another. It doesn't need a reference point, because it's not an absolute value. SNR is the ratio of signal power to noise power, and attenuation is the ratio of transmitted power to received power. Both are normally expressed (quite correctly) in decibels.

The fact that many people misuse decibels is not a point which has relevance here, and I wouldn't want people reading the article to be confused by the last few messages. The article was a serious attempt to explain a technical subject in reasonably simple terms, and it doesn't misuse the term dB in any way.